This tier list is subject to opinion. It is taken from VibratingSheep's list here. This list focuses on the early game, through Hard/Very Hard fights. Assume that characters have 1-2 uncaps (3rd skill + 1st skill upgraded), or maybe a full uncap if you push hard for it.
Yuel - Heals, double attacks a lot, and lets you get to work on the level grinding towards her 5*.
Percival - Fear is ridiculous and he has a solid nuke and buff. Core Fire unit.
Metera (Fire) - Stuff is going to have trouble surviving her stock turns and she has useful statuses.
Aoidos - Great at mowing stuff down with Bloody Garden when it can't kill him fast enough in return.
Altair - Really good buffs and ougi gen works well at any point, and his mist will actually see use before you get Dark Fencer.
Lancelot - Debuffing nuke, high CA rate, and one of the highest attack stats out there.
Lilele - Another powerful buffer. Make sure the MC is Gran! All three of these characters could be considered core.
Aletheia - Good nukes, 5-turn Ignition, doesn't kill himself in the process.
Sara - Ultimate tank, good luck dying once you get her third skill. One of Earth's cores and also works off element.
Eustace - Can pump his own Charge Attack damage and inflict Paralyze for 30s.
Feena - AoE Armor Break is good stuff and her Charge Attack potential is gigantic.
Petra - One of the best supports in the game, and thrives in Grande teams. Core Wind unit, and probably the most reliable Start Dash option.
Korwa - THE best support in the game, can go in any team.
Jeanne d'Arc - Has Weapon Master's two best EX skills (Rage III, Armor Break), with a 100% TA skill cherry on top. Core light unit.
Albert - Always at least doubles, charged nukes deal massive damage, and a Delay.
Amira - Her ability to increase the team's multiattack rate and charge bar generation is always nice, and can mini-duration things to charge even faster. Also lets you get to work on her 5*. Core light unit.
Narmaya - Plenty of damage and good utility. Be aware that she's fairly complex and really wants level 55.
Vania - While one of her biggest upsides isn't relevant yet, she still brings plenty of utility and a hard-hitting Charge Attack if the target is charmed. Core Dark unit.
Vaseraga - Huge attack stat and completely trashes enemies that dare enter Overdrive.
Forte - Skill 2 is good early when better stuff doesn't overwrite it, and she has plenty of offense between her passive and potential double nuke.
Clarisse - Her third skill doesn't do much early game, but 25% def down and a plain damage nuke still do work.
Zahlhamelina - If you pull another good fire unit or two you're in business, just don't kill yourself with Flare.
Magisa - Good utility but a lot of her power is backloaded, especially behind her 5*.
Silva - Huge Charge Attack damage, but when you're grinding through the story her 2nd skill will be mostly unusable.
Charlotta - Not quite the powerhouse that is the top 3, but Armor Break, Burst Drive, and 50% damage cut are all effective.
Yngwie - Does Real Man things, but early on you will usually find Tough Guy mode unsustainable due to lacking charge generation.
Cagliostro - See Magisa. She's really good at healing but a lot of her power is locked behind 5*. Core Earth unit eventually.
Catherine - Has to work for her assassins, but hey, charm and your choice of ODA/BA.
Nemone - Dodgetanks for your team while charging up for huge damage. Fairly straightfoward and strong.
Ayer - Countertank that works really well early when he can set up at lower HP safely.
Siegfried - Getting Sieg early means you get to work on his 5*, but the grind there is painful.
Nezahualpilli - While you can't fix his glass cannon problems until level 100, you can still delete things with Break Assassin and a huge attack stat. If you happen to get this guy+Petra you can just have Petra cast Illusion on him and go nuts. Core Wind unit.
Agielba - You probably don't want your strongest unit to be sitting around at low health like he wants to, although he does lots of damage if he can get away with it.
Zeta - Completely relies on the enemy being in Break.
Ghandagoza - Kinda RNG reliant tanking and won't save your team from Charge Attacks, but his Blind stacks with other blinds and he can dish it out if the enemy targets him.
Lily - Heal and AoE is nice but her attack is abysmal for a SSR, and her first skill won't see much use early since it only works against Fire.
Societte - A preview of Dark Fencer with a single-target heal, but her 2nd skill doesn't stack with mist and DF will be FAR more accurate with it.
Arulumaya - Suited more towards the late game with her Veil. AR2 and Delay are nice but nothing to get excited over.
Melleau - Earth has enough good attackers and charge generators that her weaknesses show in comparison. Recent updates have made her MUCH better, at least.
Hallessena - Hits hard but needs some form of protection to truly shine.
Gawain - If you need to survive something, he'll do a good job. If you need to kill things, not so much unless your entire team is nearly dead. The problem is that wind can get very good at blitzing things very fast with the right units.
Lennah - Good heal especially since it's the element that covers Catalina's weakness and that's about it. Low CD Clear isn't needed early.
Sarunan - He's got an AoE nuke to clear story trash, but his Dark Resist and Break Lock aren't needed early on.
Beatrix - Really complex, and fights generally won't last long enough for her to shine.
Cerberus - Nukes are good at the moment but the numbers on her skill 3 are terrible (low hit rates on the important statuses)